1. Technical Field
The present invention relates to cavities and channel add/drop filters employing photonic crystals (PCs), and in particular to improvements in the characteristics of cavities and channel add/drop filters based on two-dimensional photonic crystals.
2. Description of the Related Art
It should be understood that in the present specification, the significance of the term “light” is meant to also include electromagnetic waves that relative to visible light are of longer as well as shorter wavelength.
Along with advances in wavelength division multiplexed (WDM) optical communication systems in recent years, the importance of ultrasmall add/drop filters and channel filters in which enlarged capacity is being targeted is on the rise. In this area, then, attempts are being made to develop extraordinarily small-scale optical add/drop filters by employing photonic crystals. In particular, with photonic crystals novel optical properties can be realized by exploiting artificial periodic structures in which a crystal-lattice-like periodic refractive index distribution is artificially imparted within the parent material.
One important feature of photonic crystals is the presence of photonic bandgaps. With photonic crystals having three-dimensional refractive index periodicity (3D photonic crystals), perfect bandgaps in which the transmission of light is prohibited in every direction can be formed. Among the possibilities with these crystals are the local confinement of light, control of spontaneous emission, and formation of waveguides by the introduction of line defects, wherein the realization of ultrasmall photonic integrated circuits can be anticipated.
Meanwhile, studies into uses for photonic crystals having a two-dimensional periodic refractive-index structure (2D photonic crystals), are flourishing because the crystals can be manufactured comparatively easily. A periodic refractive-index structure in 2D photonic crystals can be formed by, for example, arranging in a square-lattice or triangular-lattice geometry air rods perforating a high-refractive-index plate material (usually termed a “slab”). Alternatively the structure can be formed within a low-index material by arranging, in a 2D-lattice geometry within the material, posts made of a high-refractive-index material. Photonic bandgaps can be produced from such periodic refractive-index structures, enabling the transmission of light traveling in an in-plane direction (a direction parallel to both the principal faces of the slab) to be controlled. Waveguides, for instance, may be created by introducing line defects into a periodic refractive-index structure. (See, for example, Physical Review B, Vol. 62, 2000, pp. 4488-4492.)
FIG. 10 illustrates, in a schematic oblique view, a channel add/drop filter disclosed in Japanese Unexamined Pat. App. Pub. No. 2001-272555. (In the drawings in the present application, identical reference marks indicate identical or equivalent parts.) The channel add/drop filter in FIG. 10 exploits a 2D photonic crystal having, configured within a slab 1, cylindrical through-holes 2 of identical diameter (ordinarily occupied by air) formed at the vertices of a 2D triangular lattice. In a 2D photonic crystal of this sort, light is prohibited from propagating in an in-plane direction within the slab 1 by a bandgap, and in the direction normal to the plane (direction orthogonal to the two principal faces of the slab) is confined due to total internal reflection occurring at the interface with the low-refractive-index clad (air, for example).
The photonic crystal in FIG. 10 contains a waveguide 3 consisting of a straight line defect. This straight-line defect 3 includes a rectilinearly ranging plurality of lattice points adjoining each other, with the through-holes 2 missing in these lattice points. With light being able to propagate through defects in the 2D photonic crystal, the straight-line defect can be employed as a linear waveguide. With linear waveguides, the spectrum of wavelengths in which light can be transmitted at low loss is comparatively broad; consequently light in a wide range of wavelengths containing signals in a plurality of channels may be propagated through such waveguides.
It will be appreciated that the width of straight-line defects as waveguides can be altered variously in accordance with the requisite characteristics. The most typical waveguide is obtained, as described above, by leaving through-holes missing in one row in the lattice-point lines. Nevertheless, waveguides can also be created by leaving through-holes missing in a plurality of neighboring rows in the lattice-point lines. Moreover, a waveguide is not limited in width to integral multiples of the lattice constant, but may have an arbitrary width. For example, it is possible to create a waveguide having a width of choice by relatively displacing the lattice on either side of a linear waveguide to the distance of choice.
The photonic crystal set out in FIG. 10 also contains a cavity 4 consisting of a point defect. The point defect 4 contains a single lattice point, and through that lattice point a through-hole that is of large diameter as compared with the other lattice points is formed. A defect in this way containing a relatively large-diameter through-hole is generally termed an acceptor-type point defect. On the other hand, a defect in which a through-hole is missing in a lattice point is generally termed a donor-type point defect. The cavity 4 is disposed adjacent the waveguide 3, within a range in which they can exert on each other an electromagnetically reciprocal effect.
In a 2D photonic crystal such as that illustrated in FIG. 10, if light 5 containing a plurality of wavelength ranges (λ1, λ2, . . . λi, . . . ) is introduced into the waveguide 3, light that has the specific wavelength λi corresponding to the resonant frequency of the cavity 4 is trapped in the cavity and while resonating in the interior of the point defect, light 6 of wavelength λi is emitted in the normal direction, in which the Q factor originating in the finite thickness of the slab 1 is small. This means that the photonic crystal in FIG. 10 can be employed as a channel drop filter. Conversely, by shining light into the point defect 4, in the direction normal to the slab 1, light of wavelength λi that resonates within the cavity 4 can be introduced into the waveguide 3. This means that the photonic crystal in FIG. 10 can also be employed as a channel add filter. It will be appreciated that the transfer of light between either the waveguide 3 or the cavity 4 and the exterior can be made to take place by proximately disposing an optical fiber or an optoelectronic transducer in the vicinity of the waveguide end faces or the vicinity of the cavity. Of course, in that case a collimating lens (collimator) may be inserted in between either the waveguide end face or the cavity, and the optical-fiber end face or the optoelectronic transducer.
In an optical add/drop filter such as that illustrated in FIG. 10, by appropriately configuring the spacing between the waveguide 3 consisting of the line defect and the cavity 4 consisting of the point defect, the ratio of optical intensities in a specific wavelength that is transferred between the waveguide and the cavity can be controlled. Also in FIG. 10, since no asymmetry is introduced with respect to the point defect 4 in the direction normal to the slab 1, light is output in both vertical directions from the point defect 4; but it is possible to make the output of light be in only one or the other vertical direction by introducing asymmetry in the point defect 4 in the plane-normal direction. An example of a mechanism that can be utilized to introduce this sort of asymmetry is a method in which the diameter of the point defect 4, which is round in section, is made to vary continuously or discontinuously along the thickness of the slab. With further regard to FIG. 10, although the channel add/drop filter in the figure contains only a single cavity, it will be readily understood that by disposing along the waveguide a plurality of cavities differing from one another in resonant wavelength, optical signals in a plurality of channels can be added/dropped.
With the Q factor of a cavity employing an acceptor-type point defect such as disclosed in Japanese Unexamined Pat. App. Pub. No. 2001-272555 being around 500, the full width at half-maximum (FWHM) in the peak-wavelength-including light output from a cavity of this sort is around 3 nm.
However, using multi-channel signals for WDM communications at about 100 GHz with a wavelength-peak spacing of approximately 0.8 nm is being investigated. This means that with a cavity such as disclosed in Unexamined Pat. App. Pub. No. 2001-272555, the largeness of the Q factor is insufficient, and with the 3-nm FWHM, the cavity is totally inadequate for separating from one another multi-channel signals whose peak-wavelength spacing is approximately 0.8 nm. In short, there is a need to raise the Q factor of cavities employing 2D photonic crystals, to reduce the FWHM of the peak-wavelength spectra they output.
Prior art cavity-tuning methodologies include that taught by Kartik Srinivasan and Oskar Painter in “Momentum space design of high-Q photonic crystal optical cavities,” Optics Express, Vol. 10, No. 15, Jul. 29, 2002, pp. 670-684. On page 673, section 3, line 3, Srinivasan and Painter state, “the geometry of the defect and the surrounding holes can be tailored to reduce . . . [radiation loss],” (that is, to raise the Q value). Srinivasan and Painter teach modifying defect geometry in three specific ways: (1) as illustrated in the left-most column of Table 6 on page 679; (2) as illustrated in the left-most column of Table 7 on page 680; and (3) as illustrated in FIG. 7(a) on page 682. In the first instance, the defect geometry is designed by enlarging the radius of the single hole constituting the defect. In the second, each of the pair of defect-constituting holes about common center e is reduced in diameter. While in the first two examples, the geometry of the lattice holes surrounding the point defect is unaltered, in the third example—a modification of the second—holes neighboring the defect are altered to create a “graded lattice.” Specifically, the immediate-neighbor holes are enlarged in radius, and “[t]he hole radii are then increased parabolically outwards for 5 periods in the {circumflex over (x)}-direction and 7 periods in the ŷ-direction, after which they are held constant (page 683, lines 2-4).
The gradating of the lattice by parabolically altering the dimension of the holes outwards for several periods from the defect is based on a methodology that precedes the Srinivasan paper. That is, what led Srinivasan and Painter to hit upon their graded cavity structure is based on the perturbation theory. The theory is one according to which, starting from a photonic crystal slab, a cavity configuration is determined by treating the introduction of a defect as a perturbation in the dielectric, and then performing a Fourier transform on the perturbation to evaluate, in a process of trial and error, whether the “leaky cavity modes” have increased. Yet a guide to approaching where and in what way is best to alter the cavity structure cannot by obtained from this technique. In other words, the result of trial and error is for the most part fortuitous; moreover, a cavity having a high Q value can only be obtained by altering the geometry of extraordinarily many air holes.
In sum, the graded cavity is designed using the perturbation theory, and accordingly, Q can only be increased by, for the most part, chance—and moreover, only by altering the size of a very large number of air holes.
A further consideration is that Srinivasan and Painter are concerned with minimizing the mode volume to the extent possible—that is, “modal volumes approaching the theoretical limit of a cubic half-wavelength” (Introduction, end of first paragraph). In particular, the Srinivasan and Painter paper is directed to PC optical microcavities having “very small mode volumes and loss properties sufficient to sustain lasing” (Introduction, second paragraph, referring to an earlier study by Painter et al.) Clearly, Srinivasan and Painter is concerned with active devices; in addition to mentioning lasers in the introduction, Srinivasan and Painter later mention “resonators.”
Thus, a design constraint on a defect cavity according to Srinivasan and Painter presents itself. That is, in order to minimize the defect mode volume so as to “approach the theoretical limit of a cubic half-wavelength,” a point-defect according to Srinivasan and Painter must be designed according to the perturbation theory. That is why, ultimately, Srinivasan teaches only two defect geometries, that of Table 6 and that of Table 7 in the Srinivasan and Painter paper. In both cases, the dimension of the defect-constituting hole(s) is altered. In the former case, the defect is constituted by a single hole that is enlarged diametrically; in the latter, the defect is constituted by a pair of holes centered on the defect's origin point and reduced diametrically. (It is to be noted that the latter cavity structure is also a single-point based defect geometry.)
PC devices according to Srinivasan and Painter—that is, PC resonators, as noted earlier—are limited to being constituted by the point defect geometries of Table 6 and Table 7 in the Srinivasan and Painter paper—that is, to geometries of enlarging a single defect-constituting hole, or reducing twinned defect-constituting holes, in order to achieve the mode-volume minimization necessary for the functioning of the resonators.
Akahane et al., “Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,” Applied Physics Letters, Vol. 82, No. 9, Mar. 3, 2003, pp. 1341-1343, is a paper directed to PC channel add/drop filters for wavelength-division multiplexed (WDM) optical communication systems. The paper notes that devices utilizing acceptor-type defects do not achieve Q high enough to provide the filtering resolution required for WDM applications, and that meanwhile researchers have concentrated efforts on improving the Q of defect cavities alone (rather than the Q of the cavity-waveguide system as a whole, functioning as a filter). Akahane et al. then references Vu{hacek over (c)}kovićet al. (“Design of photonic crystal microcavities for cavity QED”) and another paper to point out that                In such studies, the combination of the high Q factors and small mode volumes are considered very important since the goal is to realize high performance active light-emitting devices such as zero-threshold lasers, etc.In the sentence succeeding the above-quoted sentence, Akahane et al. then add, However, the requirement for the mode volume size is not essential for this channel add/drop filter [that is, the channel add/drop filters that are the focus of the Akahane et al. paper] since it is a passive device, as long as the cavity is single mode for the concerning [sic] spectral range . . . . Instead we must consider the interaction between the defect cavity and the line defect waveguide.(Emphasis added.)        
Hence, the authors of the Akahane et al. paper realized that passive PC devices have different design requirements from those of active devices—in particular that the mode volume limitations are not as severe—and determined to “investigate various donor defects with one to three missing holes which are filled with the same dielectric substance as the slab.”
Akahane et al.'s “L2” and “L3” defects, formed respectively by two missing air holes and three missing air holes, when tested in isolation (not in combination with waveguides) each demonstrated an approximately four-fold increase in Q over the defect with one fewer missing air hole. Then, referring to FIG. 2, the second column on the second page of the Akahane et al. article discusses the relationship between Q, as given by in-plane Q and vertical Q, and the separation between the defect cavity and a waveguide as constituents of a filtering device.
The Akahane et al. results seem to suggest that in applications in which the greater mode volume does not preclude a functioning device, the higher Q gained is advantageous. In particular, Akahane et al. found that the L3-based devices have very high filtering resolution and useful polarized emission characteristics.
Akahane et al. evaluated the Q of L2 and L3 (as well as L1) defect cavities in isolation, and the Q of the cavities combined with waveguides to function as filters. Regarding L2 and L3 defect cavities in isolation, Akahane et al. is completely silent as to how the Q of the cavities might be improved—in particular, Akahane et al. is totally silent about modifying the geometry of defect-surrounding holes. On the other hand, Akahane et al. does investigate and discuss how the (L3) cavity-to-waveguide separation can improve Q.
To enhance the Q of the cavities to which their research is directed, Srinivasan and Painter in the first place alter (perturb) the geometry of the single-point defects themselves. To enhance the Q further while preserving the minimal mode volume of the single-point cavities, Srinivasan and Painter then apply the known methodology of tailoring the geometry of the defect-surrounding holes—specifically, they parabolically gradate the size of the holes for several defect-concentric periods by enlarging the holes' radii.
As is clear from the Srinivasan and Painter discussion, on page 683 of their paper, of their “chosen lattice,” the relationship between the altered size of the defect-constituting hole(s) and of the size of the holes in the surrounding graded lattice is critical. (They mention that the relationship acts “as a potential well [to] confine the mode in real space.)
While Akahane et al. measures the Q of an L3 defect, the reference is silent on improving the Q of a cavity constituted by the defect. Moreover, the methodology utilized by Srinivasan and Painter is inapplicable to an L3 defect according to Akahane et al., in the first place because the defect-constituting holes are filled; the defect is constituted simply by a run of missing holes, not by altering the size of a hole on a single point or of a twinned pair about a single point. The defect-hole/defect-surrounding-hole relationship crucial to improving Q in Srinivasan and Painter is not even available for improving the Q of cavity according to Akahane et al.